Demands for high-precision measurements of a circuit element are increasing annually. The apparatus for such measurements is exemplified by the "Multi-Frequency LCR meter 4274A or 4275A" which is commercially available from Yokogawa-Hewlett-Packard for use in four-terminal measurements. FIG. 1 is a schematic circuit diagram showing a circuit element measuring apparatus for four-terminal pair measurements according to the prior art.
By means of four terminal lines CL.sub.1, CL.sub.2, CL.sub.3, and CL.sub.4 providing four terminal pairs, a circuit element to be measured (hereinafter referred to as a "DUT" or element Z.sub.x) is connected to a signal source SS, a volt meter VM, a range resistance R.sub.r and a zero detection amplifier A which together form a measuring apparatus. The impedance value of the element Z.sub.x shall also be referred to as Z.sub.x.
The lines CL.sub.1, CL.sub.2, CL.sub.3 and CL.sub.4 are generally made of coaxial cables although not limited thereto, and their outer conductor terminals g.sub.11, g.sub.21, g.sub.31 and g.sub.41 at one end thereof are connected to one another and held at the same potential. The terminals l.sub.11 and l.sub.21 of the center conductor of the lines CL.sub.1 and CL.sub.2 at the same end thereof are connected to one terminal of the element Z.sub.x. The terminals l.sub.31 and l.sub.41 of CL.sub.3 and CL.sub.4 are connected to the other terminal of the element Z.sub.x. The terminals of the center conductors of the lines CL.sub.1, CL.sub.2, CL.sub.3 and CL.sub.4 and the outer conductor at the opposite end (i.e. at the side on the meter) are respectively designated as l.sub.22, g.sub.12, l.sub.22, g.sub.22, l.sub.32, g.sub.32, l.sub.42 and g.sub.42.
Between the terminals l.sub.12 and g.sub.12, the signal source SS and a signal source resistance R.sub.s are connected in series. The volt meter VM is connected between the terminals l.sub.22 and g.sub.22. The terminals l.sub.32 and g.sub.32 are respectively connected to the inverted input terminal and non-inverted input terminal of the zero detection amplifier A. The feedback resistance R.sub.f is connected between the inverted input terminal and the output terminal of the zero detection amplifier A. The output of the zero detection amplifier A is introduced into a narrow-band amplification/phase compensation amplifier NBA. The output of the NBA is applied through the range resistance R.sub.r to the terminal l.sub.42. The NBA is similar to that used in the aforementioned meters 4274A and 4275A. The range resistance R.sub.r is placed between the terminal l.sub.42 and the NBA output, and the terminals g.sub.42 and g.sub.32 are also connected.
In the circuit of FIG. 1, an automatic control is performed on the voltage between the terminals l.sub.32 and g.sub.32, i.e., controlled such that the current flow through the terminal l.sub.32 may be substantially zero. As a result, a voltage V.sub.x to be applied to the element Z.sub.x is obtained as the indication of the volt meter VM. Moreover, a current I.sub.x to flow through the element Z.sub.x is obtained as an indication of the range resistance R.sub.r. Since a complex voltage and a complex current are measured at the volt meter VM and the range resistance R.sub.r with reference to the detected output of the signal source SS, the value Z.sub.x is determined in a complex value in accordance with the following equation: EQU Z.sub.x =V.sub.x /I.sub.x =V.sub.x R.sub.r /V.sub.i ( 0),
wherein V.sub.i is equal to the voltage generated across the R.sub.r and is expressed as EQU V.sub.i =I.sub.x R.sub.r.
The method of measuring the complex voltage or current is well known in the art and is used together with the overall operations of the meter in the aforementioned 4274A or 4275A. The calibrations are carried out by the known method of replacing the measured element with a "short" or "open" or by using a known third impedance.
It will be understood that the range resistance R.sub.r is selected to have a magnitude close to that of the Z.sub.x. This provides the advantage of a uniform dynamic range for succeeding volt meters by making the magnitudes of the V.sub.x and V.sub.i same.
It will also be understood that the stabilization of the automatic control loop composed of the line CL.sub.3, the zero detection amplifier A, the NBA, the range resistance R.sub.r and the line CL.sub.4 can be made excellent by selecting a sufficiently small value of the feedback resistance R.sub.f.
Reference will now be made to FIG. 2 wherein a noise model of the automatic control loop of FIG. 1 is shown so as to provide an understanding of the problem of noise in the prior art thus far described. Referring to FIG. 2, reference characters E.sub.1 and E.sub.2 designate the thermal noise of the resistors R.sub.r and R.sub.f respectively; and characters E.sub.n and I.sub.n designate an equivalent input noise voltage and an equivalent input noise current of the zero detection amplifier A respectively. These four noise sources are deemed to be random and therefore have no correlation among themselves. Moreover, the individual noise sources are considered as white noise sources, as will be expressed by the following theoretical equations. ##EQU1## wherein: k is Boltzmann's constant = 1.38 .times. 10.sup.-23 [W s/K];
T is absolute temperature [K]; and PA1 f is observation band width [Hz]. PA1 q is electron charge = 6.02 .times. 10.sup.31 19 [C]; PA1 I.sub.c is collector current [A]; and PA1 h.sub.FE is short-circuit current gain. PA1 f is measurement frequency. PA1 SR is the slew rate; PA1 C.sub.t = C.sub.1 +C.sub.2 ; PA1 I.sub.C is the DC bias current to flow through the first stage amplification elements.
In case the amplification element at the first stage of the zero detection amplifier A is a bipolar transistor (BT.sub.4), ##EQU2## wherein: re is kT/(q.multidot.I.sub.c), kT/q = 25 mV (T = 300 K);
In case the first-stage amplification element of the amplifier A is a field effect transistor (i.e., FET), ##EQU3## wherein g.sub.m is mutual conductance [S]of the FET. The value I.sub.n can usually be ignored.
If a volt meter VI is one for measuring the voltage V.sub.i, the summation V.sub.n of the noise measured by the volt meter VI is deduced in the following form because the individual noise sources have no correlation: EQU V.sub.n.sup.2 =E.sub.1.sup.2 +(R.sub.r .multidot.E.sub.2 /R.sub.f).sup.2 +(R.sub.r .multidot.I.sub.n).sup.2 +(R.sub.r .multidot.E.sub.n /(Z.sub.x //R.sub.f)).sup.2 ( 6)
wherein, x//y is the parallel connection xy/(x+y). From Equation (6), it is found that the V.sub.n.sup.2 increases more the smaller R.sub.f is as compared with R.sub.r in the case of R.sub.r &lt;Z.sub.x. It is, therefore, advisable that the R, should not be less than the R.sub.r.
In order that an increase of the summation V.sub.n because of the noises E.sub.n and I.sub.n of the amplifier A may not be more than 3 dB, the two terms of the latter half of the Equation (6) must not be larger than the two terms of the former half: EQU (R.sub.r .multidot.I.sub.n).sup.2 +(R.sub.r .multidot.E.sub.n /(Z.sub.x //R.sub.f)).sup.2 &lt;E.sub.1.sup.2 +(R.sub.r .multidot.E.sub.2 /R.sub.f).sup.2 ( 7)
Since the values E.sub.n and I.sub.n of the Equation (7) provide no simultaneous major causes of noise, the following necessary conditions are obtained by setting I.sub.n + O or E.sub.n +O: EQU E.sub.n.sup.2 &lt;((Z.sub.x //R.sub.f))/R.sub.r).sup.2 (E.sub.1.sup.2 +(R.sub.r .multidot.E.sub.2 /R.sub.f).sup.2) (Voltage Noise Condition)(8) EQU I.sub.n &lt;(l/R.sub.r).sup.2 (E.sub.1.sup.2 +(R.sub.r +E.sub.2 /R.sub.f).sup.2) (Current Noise Condition) (9)
Although FETs have a sufficiently small I.sub.n but few FETs have a smaller E.sub.n than 2nV/ (Hz) and an FET is less suitable than the BT.sub.r (i.e., bipolar transistor) for the measurement of the DUT of a lower impedance because of higher DC bias current is needed.
By using the relations among Equations (1) to (4), (8) and (9), the bias conditions for the BT.sub.r may be determined as follows: EQU 25mV/2.times.(R.sub.r //R.sub.f)/(Z.sub.x //R.sub.f) &lt;I.sub.c &lt;2.times.25mV.times.h.sub.FE /(R.sub.r //R.sub.f) (10)
If a DUT having Z.sub.x = 50.OMEGA., for example, is to be measured, a suitable setting is R.sub.r = R.sub.f 50.OMEGA.for reasons previously described. If a BT.sub.r having h.sub.EF = 100 is used at the first stage of the amplifier A, the following relations are obtained from Equation (10) so that the noises of the amplifier A may not increase the V.sub.n to 3 dB or more. EQU 0.5mA&lt;I.sub.c &lt;200mA (11)
Likewise, the following relations are obtained if a BT.sub.r having h.sub.FE = 100 is used at the first stage of the amplifier A for the measurements of Z.sub.x = I.OMEGA.and R.sub.r = R.sub.f = 10K.OMEGA.: EQU 0.0025mA&lt;I.sub.c &lt;1mA (12)
As can be found from Equations (11) and (12) optimum value for the bias current I.sub.c of the amplification element at the first stage of the amplifier A is different for the case, in which a DUT of a low impedance is to be measured, and for the case in which a DUT of a high impedance is to be measured. In the prior art, the bias current I.sub.c uses a fixed value but not the proper value. Next, the slew rate of the amplifier A is to be considered. In FIG. 1, it is necessary for the convergence of the aforementioned automatic control loop that the input voltage of the amplifier A be sufficiently close to zero. When the DUT is to be measured with a high measurement frequency and/or a large measurement current, the change of the I.sub.x per unit time is enlarged. If the slew rate of the amplifier A becomes smaller, the amplifier A cannot absorb more than a portion of the I.sub.x. Then, the automatic control loop may perform in a nonlinear fashion and fail to converge.
The output voltage V.sub.o of the amplifier A can be expressed as the following function of time t. ##EQU4## wherein: I.sub.x is measured current (rms);
When the output voltage V.sub.o is differentiated with time, ##EQU5##
The slew rate of the amplifier A has to be larger than the maximum ##EQU6## FIG. 3 is a more detailed circuit diagram of the amplifier A. In FIG. 3, the transistor T.sub.r has its collector and emitter connected with power sources V.sub.cc and V.sub.ee through current sources CS.sub.1 and CS.sub.2 of the prior art, respectively. The emitter of the transistor T.sub.r is further connected through a bypass capacitor C.sub.o with the terminal g.sub.32 (at ground). The base of the transistor T.sub.r is the inverted input terminal of the amplifier A. A base-collector capacitor C.sub.1 and an output capacitor C.sub.2 are parasitic to the transistor T.sub.r. The output of the amplifier A is led out from the collector of the transistor T.sub.r through a buffer amplifier A.sub.1. The slew rate of the circuit of FIG. 3 is determined by the transistor T.sub.r and the peripheral circuit, as follows. EQU SR=I.sub.c /C.sub.t ( 15)
Wherein:
Our experiments have revealed it difficult to improve the SR drastically even with another structure of the amplifier A. In order that the automatic control loop may properly operate, it is necessary that Equation (15) &gt; Equation (14). ##EQU7##
In the case of Z.sub.x = R.sub.r = R.sub.f =50.OMEGA., I.sub.x = 50 mA, f = 50 MHz and C.sub.t = 20 pF, for example, the following relation has to hold. EQU I.sub.c &gt; 22 mA
In order to make possible the measurement of a high frequency and a high current, as has been described hereinbefore, it is necessary to minimize the R.sub.f and to sufficiently maximize the DC bias current I.sub.c flowing through the first stage of the amplifier A. In case an FET is used at the first stage of the amplifier A, the DUT cannot be properly measured in the high frequency and with the large current because the I.sub.c is limited by the I.sub.DSS of the FET. If, on the other hand, the I.sub.c is increased, the noise I.sub.n is augmented irrespective of the frequency.
The description thus far made could be summarized in the following form. In case that the BT.sub.r is used at the first stage of the amplifier A, the current measurement noise when a large impedance is to be measured is increased as seen from Equation (10) for a high DC bias current I.sub.c. For a low bias current I.sub.c, on the other hand, the SR necessary for measurements with the high current and the high frequency is sufficiently short as may be seen from Equation (16) so that the automatic control loop is sufficiently destabilized to make the measurements impossible. Moreover, the FET is improper for the DUT of a low impedance or for the measurements with high frequency and high current.
In the case of the products of the prior art, both the BT.sub.r and the FET are used at the first stage of the amplifier A. However, the bias current value is fixed at a suitable compromising value so that the E.sub.n and the I.sub.n are not proper for the measurements of the DUT having a certain impedance. Thus, a compromise has to be made for the increase in noise for the measurement of the I.sub.x, and high-frequency and large-current measurements cannot be accomplished.
It is, therefore, an object of the present invention is to solve the above-specified problems by a circuit element measuring apparatus which executes high-frequency and large-current measurements precisely by controlling the amplifier A.